Teaching the Lerner Rule with Uncertainty

This note explains a practical approach to teaching how a form of the Lerner rule applies even when demand is uncertain. The rule brings out the distinction between the marginal cost of a unit produced and the marginal cost of an expected unit sold, which is a key distinction for properly applying the “marginal revenue equals marginal cost” principle in the presence of uncertain demand. The Lerner rule characterization also explains the differing effects of additive and multiplicative uncertainty on a firm’s profit-maximizing price, which had been a long-standing puzzle in the intellectual history of what is known as the “price-setting newsvendor” problem.